Deep learning for photoacoustic tomography from sparse data

DOI10.1080/17415977.2018.1518444zbMath1465.94008arXiv1704.04587OpenAlexW2962850795WikidataQ64322970 ScholiaQ64322970MaRDI QIDQ4990712

Markus Haltmeier, Johannes Schwab, Stephan Antholzer

Publication date: 31 May 2021

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.04587

zbMATH Keywords

inverse problemsimage reconstructionsparse dataconvolutional neural networksdeep learningphotoacoustic tomography

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Biomedical imaging and signal processing (92C55) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for inverse problems for integral equations (65R32) Neural nets and related approaches to inference from stochastic processes (62M45) Inverse problems for integral equations (45Q05)

Related Items (14)

Uniformly convex neural networks and non-stationary iterated network Tikhonov (iNETT) method ⋮ On the randomised stability constant for inverse problems ⋮ Sampling type method combined with deep learning for inverse scattering with one incident wave ⋮ Utilizing Variational Autoencoders in the Bayesian Inverse Problem of Photoacoustic Tomography ⋮ On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector ⋮ NETT: solving inverse problems with deep neural networks ⋮ A Data-Driven Iteratively Regularized Landweber Iteration ⋮ Data-consistent neural networks for solving nonlinear inverse problems ⋮ Numerical solution of inverse problems by weak adversarial networks ⋮ Big in Japan: regularizing networks for solving inverse problems ⋮ Networks for nonlinear diffusion problems in imaging ⋮ On Learned Operator Correction in Inverse Problems ⋮ Compressed Sensing Photoacoustic Tomography Reduces to Compressed Sensing for Undersampled Fourier Measurements ⋮ Deep learning architectures for nonlinear operator functions and nonlinear inverse problems

Uses Software

• k-Wave
• ImageNet
• U-Net
• AlexNet
• PRMLT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On steepest-descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations
• Variational methods in imaging
• Operator learning approach for the limited view problem in photoacoustic tomography
• Inversion of circular means and the wave equation on convex planar domains
• The Mathematics of Computerized Tomography
• A direct method for photoacoustic tomography with inhomogeneous sound speed
• On the adjoint operator in photoacoustic tomography
• A Mollification Approach for Inverting the Spherical Mean Radon Transform
• Sparsity in Inverse Geophysical Problems
• Explicit inversion formulae for the spherical mean Radon transform
• A Novel Compressed Sensing Scheme for Photoacoustic Tomography
• Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media
• Analysis of bounded variation penalty methods for ill-posed problems
• A Galerkin Least Squares Approach for Photoacoustic Tomography
• Efficient regularization with wavelet sparsity constraints in photoacoustic tomography
• Sampling Conditions for the Circular Radon Transform
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Determining a Function from Its Mean Values Over a Family of Spheres
• Iterative Methods for Total Variation Denoising
• Mathematics of Photoacoustic and Thermoacoustic Tomography
• Thermoacoustic tomography with variable sound speed
• Analysis of Iterative Methods in Photoacoustic Tomography with Variable Sound Speed
• Inversion of Spherical Means and the Wave Equation in Even Dimensions
• Universal Inversion Formulas for Recovering a Function from Spherical Means
• Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed
• A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
• Fourier reconstruction in optoacoustic imaging using truncated regularized inverse k -space interpolation
• Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors

This page was built for publication: Deep learning for photoacoustic tomography from sparse data